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A230549
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Coins left after packing twin hearts patterns into n X n coins.
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6
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4, 5, 8, 13, 12, 21, 32, 33, 40, 57, 48, 69, 84, 85, 96, 125, 108, 141, 160, 161, 176, 217, 192, 237, 260, 261, 280, 333, 300, 357, 384, 385, 408, 473, 432, 501, 532, 533, 560, 637, 588, 669, 704, 705, 736, 825, 768, 861
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,1
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COMMENTS
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Twin hearts (6c4a type) is one of total 17 distinct patterns appearing in 3X2 coins where each pattern consists of 6 perimeter parts from each coin and forms a continuous area.
a(n) is total coins left after packing twin hearts patterns (6c4a type: 6-curves cover 4 coins) into n X n coins with rotation not allowed. The total twin hearts patterns is A230548 and voids left is A230550. See illustration in links.
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LINKS
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FORMULA
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G.f.: x^2 * (-3*x^10 - 4*x^8 + 3*x^7 + 8*x^6 + 4*x^5 - x^4 + 4*x^3 + 4*x^2 + 5*x + 4)/(1+x^3)*(1-x^3)^2*(1-x^2). (conjectured). - Ralf Stephan, Oct 30 2013
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PROG
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(Small Basic)
col = 1
row = 0
For n = 2 To 100
add = 0
If Math.Remainder(n, 2) * Math.Remainder(n, 3) <> 0 Then
add = 1
EndIf
If n >= 4 And Math.Remainder(n, 2) = 0 Then
col = col + 1
EndIf
If n >= 3 And Math.Remainder(n, 3) = 0 Then
row = row + 1
EndIf
U = n * n - (col * row + add)*4
TextWindow.Write(U+", ")
EndFor
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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